If you co-signed for a debt with your spouse, the creditor can legally look to you for payment. Therefore, disputing it isn't possible unless you think the amount of the bill is wrong. You can send a letter to the bill collector by certified mail, return receipt requested, asking for an accounting and verification of the debt. If you didn't co-sign for the debt, the FTC allows you to tell the collector to cease all communication with you immediately. If you're not sure whether the bill is joint or if it's legitimate, take it to a legal professional for review.
In Georgia, your spouse's estate is responsible for paying all debts not jointly signed for by both of you. This includes funeral bills and medical expenses that came about as the result of his last illness. If you're sure you didn't guarantee or co-sign on a bill that a collector is trying to get you to pay, turn it over to the executor of your spouse's estate. The executor will send a notice to the collector that the estate is in probate, and will instruct the collector how to make a claim for payment. It then becomes the executor's responsibility to determine whether the bill is legitimate and to dispute it, if necessary.
Other Medical Expenses
Medical bills resulting from your spouse's final illness receive somewhat high priority under Georgia probate law. The first thing the executor of your spouse's estate must pay is a year's support to you. After that, the estate pays your spouse's funeral bills. Third in line are the expenses of settling the estate, and fourth are your spouse's medical bills. If the bills don't relate to his final illness, his estate must still pay them, but they'll receive less priority. You're still not responsible for paying them yourself, so you don't have to dispute them.
It occasionally happens that a decedent's estate has more bills and expenses than money and assets with which to pay them. Even in this case, you're not responsible for your spouse's bills, provided he incurred them in his own name. His estate is insolvent, or the equivalent of bankrupt. The executor will pay your spouse's highest priority debts first, and if there's no money left to pay bills that fall lower on the priority scale, those collectors will not receive payment. They still can't legally pursue you for payment, so you don't have to dispute the account.
If a loan is secured by a mortgage, such as real estate, or if your spouse had an auto loan on a vehicle, the executor may be forced to sell the asset to cover the loans. You wouldn't be responsible for the debts unless your spouse bequeathed the asset to you and you want to keep it. In this case, you would typically have to refinance the loan into your own name, but you'd need permission from the court if the estate is insolvent and some creditors aren't receiving payment.